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Bipartite Producer-Consumer Networks and the Size Distribution of Firms

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  • Wang Dahui
  • Zhou Li
  • Di Zengru

Abstract

A bipartite producer-consumer network is constructed to describe the industrial structure. The edges from consumer to producer represent the choices of the consumer for the final products and the degree of producer can represent its market share. So the size distribution of firms can be characterized by producer's degree distribution. The probability for a producer receiving a new consumption is determined by its competency described by initial attractiveness and the self-reinforcing mechanism in the competition described by preferential attachment. The cases with constant total consumption and with growing market are studied. The following results are obtained: 1, Without market growth and a uniform initial attractiveness $a$, the final distribution of firm sizes is Gamma distribution for $a>1$ and is exponential for $a=1$. If $a

Suggested Citation

  • Wang Dahui & Zhou Li & Di Zengru, 2005. "Bipartite Producer-Consumer Networks and the Size Distribution of Firms," Papers physics/0507163, arXiv.org.
  • Handle: RePEc:arx:papers:physics/0507163
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    File URL: http://arxiv.org/pdf/physics/0507163
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    References listed on IDEAS

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    1. Fujiwara, Yoshi & Di Guilmi, Corrado & Aoyama, Hideaki & Gallegati, Mauro & Souma, Wataru, 2004. "Do Pareto–Zipf and Gibrat laws hold true? An analysis with European firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 197-216.
    2. Fujiwara, Yoshi & Aoyama, Hideaki & Di Guilmi, Corrado & Souma, Wataru & Gallegati, Mauro, 2004. "Gibrat and Pareto–Zipf revisited with European firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 112-116.
    3. Guilmi, Corrado Di & Gallegati, Mauro & Ormerod, Paul, 2004. "Scaling invariant distributions of firms’ exit in OECD countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 334(1), pages 267-273.
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    Cited by:

    1. Abu Naser Chowdhury & Po-Han Chen & Robert Tiong, 2011. "Analysing the structure of public-private partnership projects using network theory," Construction Management and Economics, Taylor & Francis Journals, vol. 29(3), pages 247-260.

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